1,300 prompts matching "Simplifying an algebraic fraction with index rules"
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Show All Working: Solving a quadratic by completing the square
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Common Mistakes: Proving that a quadratic expression is positive for every real x
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Worked Example: Finding one over alpha plus one over beta
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Show All Working: Finding a coefficient given a stated relation between the roots
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Common Mistakes: Symmetric functions when the three roots of a cubic are involved
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Worked Example: Evaluating a polynomial by substitution
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Practice: Factorising a cubic completely once one factor is known
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Show All Working: Solving a cubic equation by factorisation
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Worked Example: The sum of the products of the roots of a cubic taken two at a time
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Practice: Finding the third root of a cubic when two are known
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Show All Working: Three roots in arithmetic progression in a cubic
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Common Mistakes: Three roots in geometric progression in a cubic
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Worked Example: Solving a quadratic inequality by sketching the parabola
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Practice: Choosing a committee that must contain one particular person
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Common Mistakes: Selections in which at least one of a kind must appear
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Common Mistakes: Expressing a cos x plus b sin x in the form R cos of x minus alpha
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Show All Working: Solving a cos x plus b sin x equals c by the R method
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Common Mistakes: Giving the general solution of a trigonometric equation
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Practice: The effect of a in y equals a sin x
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Show All Working: Reading the solutions of a trigonometric equation off a graph
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